Flex in cross sectional area curves and shoulder waves

[PieroF]

Dear all,

since long time I try to brainstorm and recap an input I had years ago about shoulders of cross sectional area curve and the generated wave system.

If I remember well the idea is where to position the flexes and the points of maximum curvatures along the cross sectional area curve.

The principle is to have wave crests where the bow wave system is presenting an hollow and vice versa.

In my idea:
- the point of maximum derivative (where the second derivative changes sign and the cross sectional area curve has a flex), is the point where the hull generates pressure and therefore a local crest. This because the rate of increase of cross sectional area is maximum.
- the point where the curvature is maximum is the point where the highest velocity are expected, and therefore the minimum pressure. Here I expect an hollow...

Does anybody has indications / rules of thumbs or may contradict me in this?

How do you chose the position of these points?

Thanks!!!
PieroF

 

[jehardiman]

Yes, what you have proposed has been investigated and found not to be that exact. This is because the curve of areas does not exactly determine the points of pressure inflection along the hull (especially in viscous flow). Think of it this way...I could have the exact same curve of areas for square bottom, v bottom, round bottom, or any other form and they would have widely varying wave trains. That is not to say that closely similar hull shapes with closely similar curves of area don't have closely similar wave trains, but that is for other reasons than the curve of areas alone. If you want a good example of when something like this was first proposed, investigate Colin Archer's Wave Form Theory.